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X₂₅₀₈¶

RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}

X₂₅₀₈ (RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2508 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02508(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2508 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE} on reference triangle ABC."""
            X_2508 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(a**(8) - b**(8) - c**(8) + b**(2)*c**(2)*(b**(4) + c**(4) - a**(4))))', ID="X_2508", classes=["selected", "target"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_804 = eval_trilinear_point(model, A, B, C, 'a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))', ID="X_804", classes=["center", "incident"])
            central_line(model, X_115, X_804, 115, 804, incident=True)
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_2032 = eval_trilinear_point(model, A, B, C, '((3 + 5*cos(4*omega)  )*sin(A) + (2*sin(2*omega)  - 3*sin(4*omega)  )*cos(A))', ID="X_2032", classes=["center", "incident"])
            central_line(model, X_512, X_2032, 512, 2032, incident=True)
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            X_2485 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(4) + c**(4) - a**(4)))', ID="X_2485", classes=["center", "incident"])
            central_line(model, X_525, X_2485, 525, 2485, incident=True)
            return promote_point_to_top(model, X_2508)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2508 on the given reference triangle."""
            model = create_model('X_2508 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02508(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02508.json"))
            write_center_svg(
                model_acute,
                here / "x-02508.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2508¶

X₂₅₀₈¶